Question

Charlene puts together two isosceles triangles so that they share a base, creating a kite. The legs of the triangles are 10 inches and 17 inches, respectively. If the length of the base for both triangles is 16 inches long, what is the length of the kite’s other diagonal?

Answer 1

Answer: D

Explanation:

it is D - 21 inches

Answer 2

This is the concept of trigonometry and its identities;
We are required to calculate the length of the kite's diagonals;
Here we use the trigonometric identities;
let theta=x
tan x=opposite/adjacent
opposite=17
adjacent=10
thus
tan x=17/10
x=tan^-1 17/10
x=59.54
Therefore half the length of the diagonal will be given by:
sin x=h/10
h=10 sin x
h=10 sin 59.54
h=8.62
thus the length of the diagonal will be:
2*8.62
=17.24 in